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  <div class="section" id="numpy-sinc">
<h1>numpy.sinc<a class="headerlink" href="#numpy-sinc" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.sinc">
<code class="sig-prename descclassname">numpy.</code><code class="sig-name descname">sinc</code><span class="sig-paren">(</span><em class="sig-param">x</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/lib/function_base.py#L3245-L3316"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.sinc" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the sinc function.</p>
<p>The sinc function is <img class="math" src="../../_images/math/4d5cf2ab16913b844f6ee01023108b71f371d543.svg" alt="\sin(\pi x)/(\pi x)"/>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>x</strong><span class="classifier">ndarray</span></dt><dd><p>Array (possibly multi-dimensional) of values for which to to
calculate <code class="docutils literal notranslate"><span class="pre">sinc(x)</span></code>.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray</span></dt><dd><p><code class="docutils literal notranslate"><span class="pre">sinc(x)</span></code>, which has the same shape as the input.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p><code class="docutils literal notranslate"><span class="pre">sinc(0)</span></code> is the limit value 1.</p>
<p>The name sinc is short for “sine cardinal” or “sinus cardinalis”.</p>
<p>The sinc function is used in various signal processing applications,
including in anti-aliasing, in the construction of a Lanczos resampling
filter, and in interpolation.</p>
<p>For bandlimited interpolation of discrete-time signals, the ideal
interpolation kernel is proportional to the sinc function.</p>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r317c588351f3-1"><span class="brackets">1</span></dt>
<dd><p>Weisstein, Eric W. “Sinc Function.” From MathWorld–A Wolfram Web
Resource. <a class="reference external" href="http://mathworld.wolfram.com/SincFunction.html">http://mathworld.wolfram.com/SincFunction.html</a></p>
</dd>
<dt class="label" id="r317c588351f3-2"><span class="brackets">2</span></dt>
<dd><p>Wikipedia, “Sinc function”,
<a class="reference external" href="https://en.wikipedia.org/wiki/Sinc_function">https://en.wikipedia.org/wiki/Sinc_function</a></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">41</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">sinc</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="go"> array([-3.89804309e-17,  -4.92362781e-02,  -8.40918587e-02, # may vary</span>
<span class="go">        -8.90384387e-02,  -5.84680802e-02,   3.89804309e-17,</span>
<span class="go">        6.68206631e-02,   1.16434881e-01,   1.26137788e-01,</span>
<span class="go">        8.50444803e-02,  -3.89804309e-17,  -1.03943254e-01,</span>
<span class="go">        -1.89206682e-01,  -2.16236208e-01,  -1.55914881e-01,</span>
<span class="go">        3.89804309e-17,   2.33872321e-01,   5.04551152e-01,</span>
<span class="go">        7.56826729e-01,   9.35489284e-01,   1.00000000e+00,</span>
<span class="go">        9.35489284e-01,   7.56826729e-01,   5.04551152e-01,</span>
<span class="go">        2.33872321e-01,   3.89804309e-17,  -1.55914881e-01,</span>
<span class="go">       -2.16236208e-01,  -1.89206682e-01,  -1.03943254e-01,</span>
<span class="go">       -3.89804309e-17,   8.50444803e-02,   1.26137788e-01,</span>
<span class="go">        1.16434881e-01,   6.68206631e-02,   3.89804309e-17,</span>
<span class="go">        -5.84680802e-02,  -8.90384387e-02,  -8.40918587e-02,</span>
<span class="go">        -4.92362781e-02,  -3.89804309e-17])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">sinc</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
<span class="go">[&lt;matplotlib.lines.Line2D object at 0x...&gt;]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Sinc Function&quot;</span><span class="p">)</span>
<span class="go">Text(0.5, 1.0, &#39;Sinc Function&#39;)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">&quot;Amplitude&quot;</span><span class="p">)</span>
<span class="go">Text(0, 0.5, &#39;Amplitude&#39;)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">&quot;X&quot;</span><span class="p">)</span>
<span class="go">Text(0.5, 0, &#39;X&#39;)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="figure align-default">
<img alt="../../_images/numpy-sinc-1.png" src="../../_images/numpy-sinc-1.png" />
</div>
</dd></dl>

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